Question

The distance around the middle of a sphere (the circumference) equals 25.1327 in. What is the volume of the sphere?

Answer 1

Well, the volume of a sphere is given by (4/3)pi*r^3. So the question is, can we find the radius, r? Well, we've been given the circumference of a circle going around the sphere, so the radius of this circle should be the same as the radius of the sphere it is wrapped around. The circumference of a circle is 2*pi*r, so we have 2*pi*r = 25.1327. Your answer should be r = 25.1327/(2*pi), but you can throw that in the calculator.

Answer 2

Wait wait, I didn't mean that. That's not the answer, you plug that value 25.1327/(2*pi) into your formula for the volume, and that will be the answer.

Answer 3

circumference of a circle = \(\bf \Large 2\pi r\)
so find "r" first, then use it in the sphere volume equation
\(\bf 2\pi r = 25.1327 \implies r = \cfrac{25.1327 }{2\pi}\\
\textit{volume of a sphere }= \cfrac{4}{3}\pi r^3\)

Answer 4

stoop kid so 25.1324 divided by 2*pi

Answer 5

I got ahead of myself. 25.1327 divided by 2*pi will give you the radius of your sphere (equivalently, of the circle wrapped around it). But you are looking for the volume of the sphere, not the radius, so you need to take that value for the radius: r = 25.1327/(2*pi), and substitute it into your equation for the volume of the sphere: (4/3)*pi*(r^3), and THAT will give you your answer, sorry for adding to the confusion!

Answer 6

ok